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Buslaev, Vladimir Savel'evich
(1937–2012)
Statistics Math-Net.Ru
Total publications: 61
Scientific articles: 56

Number of views:
This page:5740
Abstract pages:25910
Full texts:11434
References:1433
Professor
Doctor of physico-mathematical sciences (1976)
Birth date: 19.04.1937
Keywords: mathematical methods of quantum mechanics; Schroedinger equation; spectral theory of linear operators; asymptotical methods of mathematical physics; wave propagation; nonlinear scattering.

Subject:

1) Mathematical scattering theory: trace formulas, asymptotic behavior of spectral characteristics, long-range potentials, singularities of many-particle scattering.

2) Asymptotical theory of classical wave propagation: scattering of short waves by convex obstacles, wave ropagation in wave guides.

3) Semiclassical approximation and the quantization: Maslov's operator, functional integrals, semiclassical approach to the adiabatically perturbed periodic problems, Bloch electrons in external fields, Stark–Wannie resonances semiclassical pseudodifferential operators with double discontinuous symbols and their applications to asymptotical study of the integrable models.

4) Difference equations with periodic coefficients: Semiclassical approach to Harper's equation, the monodromization instead of the monodromy.

5) Nonlinear waves: large time behavior of solutions of completely integrable equations, nonlinear scattering and the asymptotic stability of solitons for general nonlinear wave equations.

6) Main directions of current studies: Bloch electrons in externel fields, semiclassical approach to harper's equation, semiclassical pseudodifferential operators with discontinuous symbols, scattering of nonlinear waves.

Biography

Graduated from Physics Faculty of Leningrad State University in 1959 (chair of Mathematical Physics). Ph.D. — 1963 (advisers: O. Ladyzhenskaya and L. Faddeev). D.Sci. — 1973. Around 140 publications. 15 students defended Ph.D. thesis.

Prize of Leningrad Mathematical Society — 1963, 1-st Prize of Leningrad State University — 1974, State Prize of Russian Federation — 2000.
   
Main publications:
  • Formuly sledov i nekotorye asimptoticheskie otsenki yadra rezolventy dlya operatora Shredingera v trekhmernom prostranstve // Problemy matematicheskoi fiziki, LGU, 1966, vyp. 1, 82–101.
  • Ob asimptoticheskom povedenii spektralnykh kharakteristik vneshnikh zadach dlya operatora Shredingera // Izv. AN SSSR, ser. matem., 1975, t. 39, # 1, 149–236.
  • Kvaziklassicheskoe priblizhenie dlya uravnenii s periodicheskimi koeffitsientami // UMN, 1987, t. 62, vyp. 6, 77–98.
  • Rasseyanie dlya nelineinogo uravneniya Shredingera: sostoyaniya, blizkie k solitonu // Algebra i analiz, t. 4, vyp. 6, 1992, 63–102 (sovm. s G. S. Perelman).
  • Uravnenie Kharpera: monodromizatsiya bez kvaziklassiki // Algebra i analiz, 1996, t. 8, vyp. 2, 65–97 (sovm. s A. A. Fedotovym).

https://www.mathnet.ru/eng/person9201
https://ru.wikipedia.org/wiki/Buslaev,_Vladimir_Savelevich
List of publications on Google Scholar
https://zbmath.org/authors/ai:buslaev.vladimir-s
https://mathscinet.ams.org/mathscinet/MRAuthorID/191113
https://elibrary.ru/author_items.asp?authorid=5511

Publications in Math-Net.Ru Citations
2014
1. A. M. Budylin, V. S. Buslaev, “Quasi-Classical Asymptotics of Solutions to the Matrix Factorization Problem with Quadratically Oscillating Off-Diagonal Elements”, Funktsional. Anal. i Prilozhen., 48:1 (2014),  1–18  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 47:1 (2014), 1–14  isi  scopus 2
2012
2. V. S. Buslaev, S. B. Levin, “A System of Three Three-Dimensional Charged Quantum Particles: Asymptotic Behavior of the Eigenfunctions of the Continuous Spectrum at Infinity”, Funktsional. Anal. i Prilozhen., 46:2 (2012),  83–88  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 46:2 (2012), 147–151  isi  elib  scopus 13
2010
3. V. S. Buslaev, S. B. Levin, “Asymptotic behavior of eigenfunctions of the three-particle Schrödinger operator. II. Charged one-dimensional particles”, Algebra i Analiz, 22:3 (2010),  60–79  mathnet  mathscinet  zmath; St. Petersburg Math. J., 22:3 (2011), 379–392  isi  scopus 15
4. V. S. Buslaev, A. A. Pozharskii, “Homogenization in the Scattering Problem”, Funktsional. Anal. i Prilozhen., 44:4 (2010),  2–13  mathnet  mathscinet  zmath; Funct. Anal. Appl., 44:4 (2010), 243–252  isi  scopus 1
2007
5. V. S. Buslaev, V. Yu. Strazdin, “One-Dimensional Schrödinger Operator on the Half-Line: the Differential Equation for Eigenfunctions with Respect to the Spectral Parameter and an Analog of the Freud Equation”, Funktsional. Anal. i Prilozhen., 41:3 (2007),  84–88  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 41:3 (2007), 237–240  isi  scopus 2
2004
6. V. S. Buslaev, E. A. Grinina, “Some remarks about the quantum adiabatic theorem”, Algebra i Analiz, 16:4 (2004),  41–53  mathnet  mathscinet  zmath; St. Petersburg Math. J., 16:4 (2005), 639–648 4
7. V. S. Buslaev, M. V. Buslaeva, A. Grigis, “Adiabatic asymptotics of the reflection coefficient”, Algebra i Analiz, 16:3 (2004),  1–23  mathnet  mathscinet  zmath; St. Petersburg Math. J., 16:3 (2005), 437–452 3
2002
8. V. S. Buslaev, “Asymptotic comparison of differential equations”, Algebra i Analiz, 14:4 (2002),  1–18  mathnet  mathscinet  zmath; St. Petersburg Math. J., 14:4 (2003), 535–547 1
2000
9. A. M. Budylin, V. S. Buslaev, “The Gel'fand–Levitan–Marchenko equation and the asymptotic behavior of solutions of the nonlinear Schrödinger equation for large time values”, Algebra i Analiz, 12:5 (2000),  64–105  mathnet  mathscinet  zmath; St. Petersburg Math. J., 12:5 (2001), 761–789 4
1998
10. M. V. Buslaeva, V. S. Buslaev, “Singularities of the Green Function of the Nonstationary Schrödinger Equation”, Funktsional. Anal. i Prilozhen., 32:2 (1998),  80–83  mathnet  mathscinet  zmath; Funct. Anal. Appl., 32:2 (1998), 132–134  isi 2
1996
11. V. S. Buslaev, A. A. Fedotov, “The Harper equation: monodromization without quasiclassics”, Algebra i Analiz, 8:2 (1996),  65–97  mathnet  mathscinet  zmath; St. Petersburg Math. J., 8:2 (1997), 231–254 12
12. A. M. Budylin, V. S. Buslaev, “Quasiclassical integral equations and the asymptotic behavior of solutions of the Korteweg–de Vries equation for large time values”, Dokl. Akad. Nauk, 348:4 (1996),  455–458  mathnet  mathscinet  zmath 2
1995
13. A. M. Budylin, V. S. Buslaev, “Quasiclassical asymptotics of the resolvent of an integral convolution operator with a sine kernel on a finite interval”, Algebra i Analiz, 7:6 (1995),  79–103  mathnet  mathscinet  zmath; St. Petersburg Math. J., 7:6 (1996), 925–942 19
14. V. S. Buslaev, A. A. Fedotov, “Bloch solutions for difference equations”, Algebra i Analiz, 7:4 (1995),  74–122  mathnet  mathscinet  zmath; St. Petersburg Math. J., 7:4 (1996), 561–594 14
1994
15. V. S. Buslaev, A. A. Fedotov, “The complex WKB method for the Harper equation”, Algebra i Analiz, 6:3 (1994),  59–83  mathnet  mathscinet  zmath; St. Petersburg Math. J., 6:3 (1995), 495–517 27
1993
16. A. M. Budylin, V. S. Buslaev, “Quasiclassical integral equations with slowly decreasing kernels on bounded domains”, Algebra i Analiz, 5:1 (1993),  160–178  mathnet  mathscinet  zmath; St. Petersburg Math. J., 5:1 (1994), 141–158 4
1992
17. V. S. Buslaev, G. S. Perel'man, “Scattering for the nonlinear Schrödinger equation: states that are close to a soliton”, Algebra i Analiz, 4:6 (1992),  63–102  mathnet  mathscinet  zmath; St. Petersburg Math. J., 4:6 (1993), 1111–1142 60
18. V. S. Buslaev, G. S. Perelman, “Nonlinear scattering: the states which are close to a soliton”, Zap. Nauchn. Sem. POMI, 200 (1992),  38–50  mathnet  mathscinet  zmath; J. Math. Sci., 77:3 (1995), 3161–3169 15
1991
19. A. M. Budylin, V. S. Buslaev, “Quasiclassical integral equations”, Dokl. Akad. Nauk SSSR, 319:3 (1991),  527–530  mathnet  mathscinet  zmath; Dokl. Math., 44:1 (1992), 127–131 3
20. V. S. Buslaev, “Optical and acoustical Fourier processors”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 72 (1991),  135–180  mathnet  mathscinet  zmath 1
1989
21. V. S. Buslaev, L. A. Dmitrieva, “A Bloch electron in an external field”, Algebra i Analiz, 1:2 (1989),  1–29  mathnet  mathscinet  zmath; Leningrad Math. J., 1:2 (1990), 287–320 11
1987
22. V. S. Buslaev, “Semiclassical approximation for equations with periodic coefficients”, Uspekhi Mat. Nauk, 42:6(258) (1987),  77–98  mathnet  mathscinet  zmath; Russian Math. Surveys, 42:6 (1987), 97–125  isi 37
23. V. S. Buslaev, L. A. Dmitrieva, “Adiabatic perturbation of periodic potential. II”, TMF, 73:3 (1987),  430–442  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 73:3 (1987), 1320–1329  isi 14
24. V. S. Buslaev, N. A. Kaliteevskii, “Principal singularities of the $S$ matrix for a system of one-dimensional particles”, TMF, 70:2 (1987),  266–277  mathnet  mathscinet; Theoret. and Math. Phys., 70:2 (1987), 187–195  isi 5
1986
25. A. M. Budylin, V. S. Buslaev, “Asymptotic behavior of spectral characteristics of an integral operator with difference kernel on expanding domains”, Dokl. Akad. Nauk SSSR, 287:3 (1986),  529–532  mathnet  mathscinet  zmath 1
1984
26. V. S. Buslaev, E. A. Nalimova, “Trace formula in Lagrangian mechanics”, TMF, 61:1 (1984),  52–63  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 61:1 (1984), 989–997  isi 2
27. V. S. Buslaev, E. A. Nalimova, “Trace formula in general Hamiltonian mechanics”, TMF, 60:3 (1984),  344–355  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 60:3 (1984), 863–871  isi 4
28. V. S. Buslaev, “Adiabatic perturbation of a periodic potential”, TMF, 58:2 (1984),  233–243  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 58:2 (1984), 153–159  isi 27
29. V. S. Buslaev, V. V. Sukhanov, “On the asymptotic behaviour as $t\to\infty$ of the solutions of the equation $\Psi_{xx}+u(x,t)\Psi+(\lambda/4)\Psi$ with a potential $u$ satisfying the Korteweg–De Vries Equation. II.”, Zap. Nauchn. Sem. LOMI, 138 (1984),  8–32  mathnet  mathscinet  zmath 2
1982
30. V. S. Buslaev, “Wave field in the vicinity of boundary of a wide refractive waveguide”, Dokl. Akad. Nauk SSSR, 262:1 (1982),  75–78  mathnet  mathscinet 1
31. V. S. Buslaev, V. V. Sukhanov, “The Long-time asymptotic behaviour of the solutions of the Korteweg–de Vries equation.”, Zap. Nauchn. Sem. LOMI, 120 (1982),  32–50  mathnet  mathscinet  zmath 3
32. V. S. Buslaev, E. A. Rybakina, “Trace formula in Hamiltonian mechanics”, Zap. Nauchn. Sem. LOMI, 115 (1982),  40–60  mathnet  mathscinet  zmath; J. Soviet Math., 28:5 (1985), 645–659 2
1981
33. V. S. Buslaev, “Structure of the acoustics field near the surface of deep sea”, Zap. Nauchn. Sem. LOMI, 117 (1981),  98–111  mathnet  mathscinet  zmath 2
34. V. S. Buldyrev, V. S. Buslaev, “Asymptotic methods in the problems of asoustics propagation in ocean waveguide and their number realization.”, Zap. Nauchn. Sem. LOMI, 117 (1981),  39–77  mathnet  zmath 3
1979
35. V. S. Buslaev, S. P. Merkur'ev, S. P. Salikov, “Description of the pair potentials for which the scattering in the quantum system of three one-dimensional particles is free of diffractional effects”, Zap. Nauchn. Sem. LOMI, 84 (1979),  16–22  mathnet  mathscinet  zmath; J. Soviet Math., 21:3 (1983), 260–265 12
1977
36. V. S. Buslaev, “Solutions of “double soliton” type for the multidimensional equation $\Box u=F(u)$”, TMF, 31:1 (1977),  23–32  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 31:1 (1977), 293–299 4
1975
37. V. S. Buslaev, “On the asymptotic behavior of the spectral characteristics of exterior problems for the Schrödinger operator”, Izv. Akad. Nauk SSSR Ser. Mat., 39:1 (1975),  149–235  mathnet  mathscinet  zmath; Math. USSR-Izv., 9:1 (1975), 139–223 23
1974
38. V. S. Buslaev, M. M. Skriganov, “Coordinate asymptotic behavior of the solution of the scattering problem for the Schrödinger equation”, TMF, 19:2 (1974),  217–232  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 19:2 (1974), 465–476 8
1973
39. V. S. Buslaev, “Trace formula and singularities of the $S$ matrix for a system of three one-dimensional particles. Third group integral”, TMF, 16:2 (1973),  247–259  mathnet  mathscinet; Theoret. and Math. Phys., 16:2 (1973), 810–819 3
1972
40. V. S. Buslaev, “On trace formulas in multi-canal problems”, Zap. Nauchn. Sem. LOMI, 27 (1972),  47–66  mathnet  mathscinet  zmath 3
1971
41. V. S. Buslaev, “Scattered plane waves, spectral asymptotics and trace formulas in exterior problems”, Dokl. Akad. Nauk SSSR, 197:5 (1971),  999–1002  mathnet  mathscinet  zmath 10
42. V. S. Buslaev, “Potential theory and geometrical optic”, Zap. Nauchn. Sem. LOMI, 22 (1971),  175–180  mathnet  mathscinet  zmath 4
1970
43. V. S. Buslaev, S. P. Merkur'ev, “The third group integral in quantum mechanical statistics”, Trudy Mat. Inst. Steklov., 110 (1970),  29–44  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 110 (1970), 28–47 3
44. V. S. Buslaev, “Quantization and the WKB method”, Trudy Mat. Inst. Steklov., 110 (1970),  5–28  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 110 (1970), 1–27 6
45. V. S. Buslaev, S. P. Merkur'ev, “On the connection between the third virial coefficient and the $S$ matrix”, TMF, 5:3 (1970),  372–387  mathnet; Theoret. and Math. Phys., 5:3 (1970), 1216–1227 19
46. V. S. Buslaev, V. B. Matveev, “Wave operators for the Schrödinger equation with a slowly decreasing potential”, TMF, 2:3 (1970),  367–376  mathnet  mathscinet; Theoret. and Math. Phys., 2:3 (1970), 266–274 51
47. V. S. Buslaev, M. M. Skriganov, “On a characteristic property of Weyl quantization”, TMF, 2:3 (1970),  292–296  mathnet  mathscinet; Theoret. and Math. Phys., 2:3 (1970), 209–212 3
1969
48. V. S. Buslaev, S. P. Merkur'ev, “Trace equation for a three-particle system”, Dokl. Akad. Nauk SSSR, 189:2 (1969),  269–272  mathnet  mathscinet  zmath 2
49. V. S. Buslaev, “Invariant description of Maslov's canonical operator”, Dokl. Akad. Nauk SSSR, 184:1 (1969),  59–62  mathnet 3
50. V. S. Buslaev, “The generating integral and the canonical maslov operator in the WKB method”, Funktsional. Anal. i Prilozhen., 3:3 (1969),  17–31  mathnet  mathscinet  zmath; Funct. Anal. Appl., 3:3 (1969), 181–193 15
1968
51. V. S. Buslaev, “A trace formula in geodesic theory”, Dokl. Akad. Nauk SSSR, 182:4 (1968),  743–746  mathnet  mathscinet  zmath 2
1965
52. V. S. Buslaev, “Application of continuous integrals to the derivation of the short-wave asymptotic limit in diffraction problems”, Dokl. Akad. Nauk SSSR, 160:3 (1965),  566–569  mathnet  zmath 1
1964
53. V. S. Buslaev, “Short-wave asymptotic behaviour in the problem of diffraction by smooth convex contours”, Trudy Mat. Inst. Steklov., 73 (1964),  14–117  mathnet  mathscinet 10
1962
54. V. S. Buslaev, “On the short-wave asymptotic limit in the problem of diffraction by convex bodies”, Dokl. Akad. Nauk SSSR, 145:4 (1962),  753–756  mathnet  mathscinet  zmath 1
55. V. S. Buslaev, “Trace formulas for the Schrödinger operator in a three-dimensional space”, Dokl. Akad. Nauk SSSR, 143:5 (1962),  1067–1070  mathnet  mathscinet  zmath 10
1960
56. V. S. Buslaev, L. D. Faddeev, “Formulas for traces for a singular Sturm–Liouville differential operator”, Dokl. Akad. Nauk SSSR, 132:1 (1960),  13–16  mathnet  mathscinet  zmath 19
2010
57. V. M. Babich, V. S. Buslaev, A. M. Vershik, S. G. Gindikin, S. V. Kislyakov, A. A. Laptev, V. A. Marchenko, N. K. Nikol'skii, L. A. Pastur, B. A. Plamenevskii, M. Z. Solomyak, T. A. Suslina, N. N. Ural'tseva, L. D. Faddeev, V. P. Khavin, D. R. Yafaev, “Mikhail Shlemovich Birman (obituary)”, Uspekhi Mat. Nauk, 65:3(393) (2010),  185–190  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 65:3 (2010), 569–575  isi 1
2004
58. V. S. Buslaev, M. Z. Solomyak, D. R. Yafaev, “Mikhail Shlemovich Birman (on the Occasion of his 75th Birthday)”, Algebra i Analiz, 16:1 (2004),  5–14  mathnet  mathscinet  zmath; St. Petersburg Math. J., 16:1 (2005), 1–8 1
2002
59. A. A. Arkhipova, M. S. Birman, V. S. Buslaev, V. G. Osmolovskii, S. I. Repin, G. A. Seregin, N. N. Ural'tseva, T. N. Shilkin, “To the jubillee of O. A. Ladyzhenskaya”, Zap. Nauchn. Sem. POMI, 288 (2002),  5–13  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 123:6 (2004), 4523–4526 2
2000
60. V. S. Buslaev, A. M. Vershik, I. M. Gel'fand, S. G. Gindikin, O. A. Ladyzhenskaya, M. Z. Solomyak, L. D. Faddeev, D. R. Yafaev, “Mikhail Shlyomovich Birman (on his 70th birthday)”, Uspekhi Mat. Nauk, 55:1(331) (2000),  204–207  mathnet  mathscinet  zmath; Russian Math. Surveys, 55:1 (2000), 201–205  isi 2
1988
61. V. S. Buslaev, I. M. Gel'fand, O. A. Ladyzhenskaya, B. S. Pavlov, M. Z. Solomyak, L. D. Faddeev, D. R. Yafaev, “Mikhail Shlëmovich Birman (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 43:3(261) (1988),  201–202  mathnet  mathscinet; Russian Math. Surveys, 43:3 (1988), 233–235  isi 2

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